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Quiz #5DE
Semester 062
Dept of Mathematical Sciences
Stat319: Intro to Prob & Stat for Engineers & Scientists Instructor: Musawar A. Malik
Section: 1 (9-9.50am), or 2 (9-9:50am)
Name:_______________________ ID#:______________ Serial #:_____________________
Directions: This quiz is designed for 25 minutes. Please answer all questions. Please show your steps and box your final answer for
the following problem solving questions.
1. Consider an electrical component that has a failure rate of once in every 5 hours.
a. What is the mean time it takes for a failure of an electric component?
b. What is the probability that 12 hours will elapse before a component fail?
c.
Reliability is defined as the probability that a component will last up to a specific
time. If your company wants to guarantee an electric component has a reliability of
0.9500 that it will last up to x hours. Find this lifetime x.
Solution: Population is Exponential(=5)
a) =5
b) P(X > 12) = e-12/ = e-12/(5) =e-2.4 = 0.090718
b) P(X < x ) = 0.95  1-e- (x/ 5) =0.95
 x =-5*ln(1-0.95) = 14.9787 hours
2. PVC pipes are manufactured with a mean diameter of 1.01 inch and standard deviation 0.03
inch. A pipe with diameter less than 0.95 inch will not be acceptable in a housing contract.
Find the probability that a randomly selected pipe will not meet the need of a housing contract.
Solution: P(Z < (0.95-1.01)/0.03) = P(Z < -2 ) = 1- P(Z < -2 ) = 0.0228 from the z-table
3. The resistance of 1 meter of copper cable at a certain temperature is normally distributed with
mean 23.8 and standard deviation of 1.28.
a. What is the probability that a 1-meter segment of copper cable has a resistance greater than
25?
b. What is the lower quartile (25th percentile) of the resistance levels?
Solution: Population is N(=23.8, =1.28)
a) P(Z > (25.0-23.8)/1.28 ) = P(Z > 0.9375 ) = 1- P(Z < 0.94 ) =1- 0.8264 = 0.1736 from the z-table
b) P(Z < (P25-23.8)/1.28 ) = 0.25  (P25-23.8)/1.28 = -0.67 from the z-table
 P25 = -0.67(1.28) + 23.8 = -0.8576 + 23.8 = 22.9424
Quiz #5DE
Semester 062
Dept of Mathematical Sciences
Stat319: Intro to Prob & Stat for Engineers & Scientists Instructor: Musawar A. Malik
Section: 1 (9-9.50am), or 2 (9-9:50am)
Name:_______________________ ID#:______________ Serial #:_____________________
Directions: This quiz is designed for 25 minutes. Please answer all questions. Please show your steps and box your final answer for
the following problem solving questions.
4. PVC pipes are manufactured with a mean diameter of 1.01 inch and standard deviation 0.03
inch. A pipe with diameter less than 0.95 inch will not be acceptable in a housing contract.
Find the probability that a randomly selected pipe will not meet the need of a housing contract.
Solution: P(Z < (0.95-1.01)/0.03) = P(Z < -2 ) = 1- P(Z < -2 ) = 0.0228 from the z-table